New global asymptotics and anomalies for the problem of quantization of the adiabatic invariant

M. V. Karasev

Funkcionalʹnyj analiz i ego priloženiâ, Tome 24 (1990) no. 2, pp. 24-36.

Bibliographie

[1] Bakai A.S., Stepanovskii Yu.P., Adiabaticheskie invarianty, Naukova dumka, Kiev, 1981 | MR | Zbl

[2] Born M., Lektsii po atomnoi mekhanike, ONTI, M., 1934

[3] Shiff L., Kvantovaya mekhanika, IL, M., 1957

[4] Maslov V.P., Teoriya vozmuschenii i asimptoticheskie metody, MGU, M., 1965

[5] Bott R., Chern S.S., “Hermitian vector bundles and the equidistribution of the zeros of their holomorphic sections”, Acta Math., 114 (1965), 71–112 | DOI | MR | Zbl

[6] Simon B., “Holonomy, the quantum adiabatic theorem and Berry's phase”, Phys. Rev. Lett., 51 (1983), 2167–2170 | DOI | MR

[7] Berry M.V., “Quantal phase factors accompanying adiabatic changes”, Proc. R. Soc London, A392 (1984), 45–57 | MR

[8] Berry M.V., “Classical adiabatic angles and quantal adiabatic phase”, J. Phys. A: Math. Gen., 18 (1985), 15–27 | DOI | MR | Zbl

[9] Popov A.V., Transformatsiya mod v kusochno-analiticheskom volnovodnom perekhode (korotkovolnovoe priblizhenie), Preprint, no. 11, IZMIRAN, 1978

[10] Borovikov V.A., Polya v plavno neregulyarnykh volnovodakh i zadacha o variatsii adiabaticheskogo invarianta, Preprint, no. 99, IPM AN SSSR, 1978, 40 pp. | MR

[11] Buslaev V.S., “Kvaziklassicheskoe priblizhenie dlya uravnenii s periodicheskimi koeffitsientami”, UMN, 42:6 (1987), 77–98 | MR | Zbl

[12] Berlyand L.V., Dobrokhotov S.Yu., “Operatornoe razdelenie peremennykh v zadachakh o korotkovolnovykh asimptotikakh dlya differentsialnykh uravnenii s bystroostsilliruyuschimi koeffitsientami”, DAN SSSR, 297:1 (1987), 80–84 | MR

[13] Faddeev L.D., Shatashvili S.L., “Algebraicheskie i gamiltonovy metody v teorii neabelevykh anomalii”, TMF, 60:2 (1984), 206–217 | MR

[14] Jezabek M., Praszalowicz M. (eds.), Werkshop on Skyrmions and Anomalies, World Scientific, Singapore, 1987 | MR

[15] Karasev M.B., “Puassonovskie algebry simmetrii i asimptotika spektralnykh serii”, Funktsion. analiz i ego pril., 20:1 (1986), 21–32 | MR | Zbl

[16] Karasev M.V., “Svyaznosti na lagranzhevykh podmnogoobraziyakh i nekotorye zadachi kvaziklassicheskogo priblizheniya”, Zapiski nauchn. semin. LOMI, 172, 1988, 41–54

[17] Karasev M.V., “Lagranzhevy koltsa. Mnogomasshtabnaya asimptotika spektra vblizi rezonansa”, Funktsion. analiz i ego pril., 21:1 (1987), 78–79 | MR | Zbl

[18] Karasev M.V., To the Maslov theory o! quasi-classical asymptotics. Examples of new global quantization formula applikations, Preprint / ITPh. Kiev, 1989. No ITP – 89-78E, 32 pp. | MR

[19] Karasev M.B., Kvantovaya reduktsiya na orbity algebr simmetrii i zadacha Erenfesta, Preprint / ITF. AN USSR. Kiev, 1987. ITF-87-157R | MR

[20] Babich V.M., Buldyrev V.S., Molotkov I.A., Prostranstvenno-vremennoi luchevoi metod. Lineinye i nelineinye volny, LGU, L., 1985 | MR

[21] Maslov V.P., Kompleksnyi metod VKB v nelineinykh uravneniyakh, Nauka, M., 1977 | MR

[22] Arnold V.I., “Malye znamenateli i problema ustoichivosti dvizheniya v klassicheskoi i nebesnoi mekhanike”, UMN, 18:6 (1963), 91–192 | MR

[23] Arnold V.I., Kozlov V.V., Neishtadt A.I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, Itogi nauki i tekhn. Sovrem. probl. matem. Fundament. napr., 3, VINITI, M., 1985 | MR